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Irena Komprej | 1 Jan 1998 03:17

[R] Cancor

Dear R's!
I am strugling with cancor procedure in R. I cannot figure out the
meaning of xcoef and of yxcoef.
Are these:
1. standardized coefficients
2. structural coefficients
3. something else?

I have tried to simulate canonical correlation analysis by checking the
eigenstructure of the expression:

Sigma_xx %*% Sigma_xy %*% Sigma_yy %*% t(Sigma_xy).

The resulting eigenvalues were the same as the squared values of
cancor$cor. I have normalized the resulting eigenvectors, the a's with

sqrt(a'%*%Sigma_xx%*%t(a)), and similarly the b's with
sqrt(b'%*%Sigma_yy%*%t(b)).

The results differed considerably from xcoef and ycoef of the cancor.

I thought then, maybe these coefficients are structural coefficients and
therefore I multiplied them, the a's with
a%*%Sigma_xx, and the b's with
b%*%Sigma_yy,

but the results are nevertheless far from those of the cancor. Now, I
really don't know any more, how to interpret the xcoef and ycoef.
I am thanking you in advance.
(Continue reading)

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Irena Komprej | 1 Jan 1998 01:44

[R] Cancor

Dear Gabor,
thank you for your answer related to the normalization of cancor
coefficients. If you want to interpret the coefficients in terms of
variables' contributions to canonical variables, loadings, redundancy
measure, etc. ,  you have to normalize the results so that the canonical
variables have identity variance matrix. Multiplying cancor coefficients
xcoef and ycoef by as.numeric(sqrt(nrow(x)-1)) does the job.
(I sometimes miss such information in the R help.)
Best regards,
Irena Komprej

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Gmane